4. Martin GERA : "Improved representation of boundary layer"
The energy spectrum of turbulence is not homogeneous at reality. Nevertheless, we often except that turbulence is a random process with independence on position, what is a definition of homogeneous turbulent processes. Away from boundaries and from a stable stratified atmosphere this assumptions work correctly. Resolved eddies are isotropic and small energetic eddies can cascade until viscosity dissipation. In other cases anisotropy is assumed. Near the wall, the size of energetic eddies becomes proportional to the distance from this barrier. Increasing the resolution, mainly in the vertical direction, creates a problem with grid anisotropy and does not describe the situation correctly.
The showed difficulties can be partly prevented by choosing the right variables at convenient equations in numerical model. Explicit use of the turbulent kinetic energy (TKE) into equations can touch problems with energy transfer and interrelation between subgrid and resolved scale. This improves the knowledge of developing processes and enables us to put new features and relationships among diagnostic and prognostic variables. TKE directly measures an intensity of turbulence and it can afford new knowledge for parameterization. Adding this equation as prognostic equation can has positive effect for properties of parameterization, although it increases a number of unknowns. Further enhance can be done by non-local view of parameterization. Non-local approach uses not only adjacent region for parameterization. It can take into account the effects of all various sizes eddy from far-field region.
Understanding the energy transfers relationships at spectral space can yields new formulation of parameterization schemes. It allows us to examine this equation as a function of wave numbers or eddy size. We do an analysis of TKE terms individually (Borkowski, 1969,Batchelor.1953). It helps us determine a physical process, which generate turbulence and it allows us to find expressions for parameterized variables.
Result of our analyses is spectral function for E (k) and its vertical part. From these analyses is shown that energy equation presents the inertial and the buoyancy subrange well. From this investigation is obvious, that TKE gives a useful information and it is applicable for solved problem.
Full feature of presented equation can be give numerically only. We need expressions for statistical moments. We use 1 and 1/2 closures. After application a Sommerias hypotheses and tensor decomposition to the isotropic and anisotropic parts, we get formulas for present statistical moments and energy equation. Parameterization of present terms is needed for close the equations. We have information from spectral analyses, that eddy-transfer coefficient has dependence on dissipation term (epsilon).
In spite of new features, the mixing-length (L) is the still arbitrary parameter, which must vary from the LES to the Single column model [epsilon=epsilon (L)]. From computation above is seemed that introducing an equation for dissipation of energy can solve this arbitrary choice. This approach is called k-epsilon closure. Different approach for selection of L can be use, for example formulation of Bougeault and Lacarrere. These all experiences are needed for construction TKE scheme.
5. Ilian GOSPODINOV : "Reformulation of the physics-dynamics interface "
Various studies on the model dynamics
1. Predictor-corrector versus constant acceleration semi-Lagrangian trajectory scheme
Comparison study on the properties of the predictor-corrector method for the hydrostatic adiabatic model and the constant acceleration semi-Lagrangian trajectory scheme has been carried out. The activities were concentrated in implementing the constant acceleration scheme into a more recent version of the model as well as testing the response of this new configuration to extreme weather cases. The aim of this study is to demonstrate the advantages or disadvantages of each method applied to the 3D hydrostatic adiabatic model.
2. Very high resolution with a simplified model
With the help of the simplified 1D shallow water model we studied the response of the model to a very big jump in resolution going from the parent model to the coupled one. The main objective is to study the response of the model to a refined orographic forcing which is available in the very high-resolution 1D limited area model. The result of this study will highlight relevant study with the 3D model.
3. Reformulation of the physics-dynamics interface
A study of the structure of the flow of information in the model concerning the vertical velocity for both hydrostatic and non-hydrostatic model has been carried out. The vertical motion is the most sensitive part of the model dynamics and it could potentially benefit the reformulation of the physics-dynamics interface.
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